Block #1,446,483

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 2/7/2016, 12:02:54 PM · Difficulty 10.7594 · 5,396,162 confirmations

1CC
Cunningham Chain of the First Kind

A sequence where each prime is double the previous prime plus one.

Block Header
Block Hash
6f494b5409ab389a3f51027d008723eee262f12f9ae7683f0667f7655fc2d391

Height

#1,446,483

Difficulty

10.759438

Transactions

2

Size

1005 B

Version

2

Bits

0ac26a8a

Nonce

1,817,814,946

Timestamp

2/7/2016, 12:02:54 PM

Confirmations

5,396,162

Merkle Root

b8699b032cff99fcdebff75067310096ac60cb38a7e1365516dafd2eec626536
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

5.551 × 10⁹⁵(96-digit number)
55517704884292845760…91441216695307046399
Discovered Prime Numbers
p_k = 2^k × origin − 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

1
origin − 1
5.551 × 10⁹⁵(96-digit number)
55517704884292845760…91441216695307046399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.110 × 10⁹⁶(97-digit number)
11103540976858569152…82882433390614092799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.220 × 10⁹⁶(97-digit number)
22207081953717138304…65764866781228185599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
4.441 × 10⁹⁶(97-digit number)
44414163907434276608…31529733562456371199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
8.882 × 10⁹⁶(97-digit number)
88828327814868553216…63059467124912742399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.776 × 10⁹⁷(98-digit number)
17765665562973710643…26118934249825484799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
3.553 × 10⁹⁷(98-digit number)
35531331125947421286…52237868499650969599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
7.106 × 10⁹⁷(98-digit number)
71062662251894842573…04475736999301939199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.421 × 10⁹⁸(99-digit number)
14212532450378968514…08951473998603878399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
2.842 × 10⁹⁸(99-digit number)
28425064900757937029…17902947997207756799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
5.685 × 10⁹⁸(99-digit number)
56850129801515874058…35805895994415513599
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Cunningham Chain of the First Kind. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★★☆☆
Rarity
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)
Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,985,594 XPM·at block #6,842,644 · updates every 60s
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